Walsh-Hadamard Transform Coefficients Research Articles

An effective robust and imperceptible blind color image watermarking using WHT

Digital image watermarking is the most widely used recognized approach to protect data against piracy. This paper proposes a new blind color image watermarking based on the Walsh Hadamard Transform (WHT). The proposed method subdivides the image into 4 × 4 non-overlapping blocks, which are then transformed using WHT. The color image watermark is embedded in the third and fourth-row WHT coefficients using the proposed technique as a slight change in those rows may not profoundly affect the visual quality of an image. Then the difference of the third and fourth row WHT coefficients of the watermarked image is obtained. The watermark information is extracted using the attained difference value. The performance evaluation of the proposed scheme outperforms in terms of embedding capacity, Peak Signal-to-Noise Ratio (PSNR), Weighted Peak Signal-to-Noise Ratio (WPSNR), Normalized cross-correlation (NC), and Structural Similarity Index (SSIM) than the conventional watermarking methods. This proposed method provides more robustness against several manipulations and lossy attacks.

A novel blind color image watermarking based on Walsh Hadamard Transform

A new blind color image watermarking based on Walsh Hadamard Transform (WHT) is proposed in this paper which uses Triangular Vertex Transform (TVT) along with WHT. This method introduces a Triangular Vertex Transform (TVT) and Inverse Triangular Vertex Transform (ITVT) as well as applies this transform for image watermarking. Initially, convert the R, G, B color image to TVT coefficients U, V and W using the proposed TVT transform. Then the W coefficient is subdivided into 4 × 4 non-overlapping blocks, which are then transformed using WHT. The watermark is encrypted with the key K using the 2D-Logistic Sine Coupling Map encryption to obtain the encrypted watermarked image. The bits of the encrypted image is embedded in the first row WHT coefficients since the embedding of watermark bit on the first row provides high robustness to attacks. After embedding the data, the inverse WHT and inverse TVT are applied to obtain the watermarked image. The extraction process is similar to that of the embedding process where TVT is applied on the Watermarked image to construct W′ coefficient. Subdivide the attained W′ coefficient into 4 × 4 sub-block and then the WHT is applied to the 4 × 4 sub-block for extracting the data from the first row of WHT coefficients. The performance of the proposed watermarking algorithm outperforms in terms of Peak Signal to Noise Ratio (PSNR), Structural Similarity Index (SSIM) and Normalized cross-correlation (NC). Experimental results reveal that the proposed watermarking method is highly resistant to different types of attacks.

DWT–SVD–WHT Watermarking Using Varying Strength Factor Derived From Means of the WHT Coefficients

A hybrid, watermarking technique is presented in this paper. This robust watermarking technique uses discrete wavelet transform (DWT), singular value decomposition (SVD) and Walsh–Hadamard transform (WHT) together in tandem with each other. There are two novelties contained in this paper. First is the combined use of DWT, SVD and WHT, and second is the first ever use of the $$4\times 4$$ block segmentation in the robust watermarking. Another unique feature of the presented technique is that visual quality of the watermarked image has been made controllable. A varying valued strength factor having a different value for every block ( $$8\times 8$$ or $$4\times 4$$ ) of the image has been used. Proposed scheme is very secure as the safety of the embedded watermark is not compromised even if there is an interception of the side information. The proposed technique shows remarkable performance when compared with seven contemporary watermarking schemes.

Matching Level Fusion Based PalmPrint Identification using WHT and SD

 Abstract—Palmprint biometric trait is suitable to identify a person as it has more number of features compared to other biometric traits. In this paper, we propose matching level fusion based pamprint identification using WHT and SD. The pre-processing is done on palmprint images to crop ROI and resize ROI into 170×170 size. The Walsh Hadamard Transform (WHT) is applied on ROI of palmprint database and Test palmprint to derive WHT coefficients which form features. The WHT features of test palmprint are compared with Database palmprint images using Euclidean Distance (ED) to compute EER. The Spatial Domain (SD) features are obtained from ROI palmprint database and Test palmprint. The SD features of test image are compared with features of database images using ED to compute EER. The values of EER computed using WHT and SD features are fused using LogTransformation to obtain better EER. It is observed that the values of EER are zero in the proposed algorithm compared to non-zero EER values of existing algorithms.

High-Accuracy Characterization of Ambulatory Holter Electrocardiogram Events

In this paper, three noise-robust high-accuracy methods aiming at the detection and delineation of the electrocardiogram (ECG) events (QRS complex, P-wave, T-wave) were developed. The ECG signal was initially appropriately preprocessed by application of a bandpass FIR filter and Discrete Wavelet Transform (DWT). The first detection-delineation method was the Walsh-Hadamard Transform (WHT). The WHT coefficients were divided into two groups and the signal was reconstructed using the second group coefficients. By this reconstruction, the values of first derivative of events are made stronger rather than the values of other parts of signal. In the second method, a feed forward artificial neural network was implemented to detect all events of the ECG signal. In the third method, the first derivative of signal was computed using a new signal smoothing algorithm with corresponding statistical properties. For decreasing False Positive (FP) errors associated with P-wave detection, a discriminating border was introduced as the post processing stage specified by three QRS parameters: the duration of a QRS complex, the time distance from the former and latter QRS complexes, and the potential difference from former QRS complex J-location and the latter QRS complex fiducial location. The proposed methods were applied to DAY general hospital high resolution holter data.

Illumination normalisation for face recognition in transformed domain

Proposed is an illumination normalisation approach based on the block-wise Walsh-Hadamard transform (WHT) for face recognition under illumination variations. An appropriate number of low-frequency WHT coefficients is zeroed to compensate for illumination variations. Experimental studies demonstrate that the proposed method outperforms the discrete cosine transform in the cases with larger illumination variations, while for the cases with less illumination variations the method can still obtain comparable performances with a lower computational cost. Furthermore, both analytical proof and experimental results demonstrate that the principal component analysis and the null-space-based linear discriminant analysis can be directly implemented in the WHT domain to reduce further the computational cost.

WHT-based composite motion compensated NTSC interframe direct coding

The motion compensated interframe differential pulse code modulation (DPCM) and discrete cosine transform (DCT) hybrid (MC DCT) coding was nominated as a standard scheme for component TV signals by ISO and ITU-R. However, in cases where an NTSC composite TV signal is used such as the United States and Japan, applying the MC DCT scheme with its luminance/chrominance separating and composing process causes unavoidable quality degradation. The reason for this additional process required for MC DCT is that a composite TV signal presents a "color subcarrier phase shift problem" in which the color subcarrier phase varies between a coding block and reference block according to the motion vector. In this paper, we propose a Walsh Hadamard transform (WHT)-based composite motion compensated NTSC interframe direct coding scheme. In this scheme, phase shifts of a color subcarrier and modulated chrominance components between a coding block and reference block can be effectively compensated by a simple process of coefficient permutation and polarity changes of several pairs of WHT coefficients to which 100% of the subcarrier energy and most of the modulated chrominance component's energy are packed. In the motion compensated DCT scheme, however, the energy of the color subcarrier and modulated chrominance components are spread over too many coefficients and a pair-based coefficient handling rule is not given to solve this problem. This paper demonstrates that the proposed scheme provides higher coding performance for a composite NTSC signal than does the motion compensated DCT scheme with its luminance/chrominance separating and composing process.

Fast computation of discrete Hartley transform via Walsh–Hadamard transform

A new fast algorithm is proposed to compute the discrete Hartley transform (DHT) via the Walsh–Hadamard transform (WHT). The processing is carried out on an interframe basis in (N × N) data blocks, where N is an integer power of two. The WHT coefficients are obtained directly, and then used to obtain the DHT coefficients. This is achieved by a transform matrix, the H-transform matrix, which is ortho-normal and has a block-diagonal structure. A complete derivation of the block-diagonal structure for the H-transform matrix is given.